Sune Luus (27) will skipper the squad in the absence of van Niekerk, who also missed the 2022 50-overs World Cup after suffering a broken ankle in January last year.
"Dane was given an extensive opportunity to meet the minimum criteria, or the fitness benchmark for eligibility into the World Cup," women's selection convener Clinton du Preez told reporters on Tuesday.
"She recently did another fitness test and unfortunately did not meet the minimum criteria, and therefore she's missed out."
The team fitness standards require a player to run 2 km in nine minutes and 30 seconds, a mark which van Niekerk could not achieve, according to reports.
Fellow all-rounder Luus is leading South Africa in the ongoing home tri-series involving India and West Indies but van Niekerk was widely expected to return for the T20 World Cup.
Kapp on compassionate leave
The team have given all-rounder Marizanne Kapp compassionate leave as van Niekerk is her wife.
"The leave was granted so she can come back ready to play," South Africa coach Hilton Moreeng told the BBC.
"She needed a break for compassionate leave and it was granted to her because we felt we are very happy with the form she is in, as far as her skills are considered."
Kapp will not play in the final T20 of a triangular series against India.
"She (Kapp) is part of the World Cup (and) she is committed to the World Cup cause," Moreeng added.
South Africa begin their campaign against Sri Lanka in Cape Town on February 10th.
New Zealand, Bangladesh and reigning champions Australia are the other teams in Group A.
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